Finding a Starting Vertex for the Reverse Cuthill-McKee Method for Bandwidth Reduction: A Comparative Analysis Using Asymmetric Matrices

Oliveira, Sanderson L. Gonzaga de; Abreu, Alexandre A. A. M. de; Robaina, Diogo T.; Kischinhevsky, Mauricio

doi:10.1007/978-3-319-95162-1_9

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…for each matrix i, where β[max](i) is the widest bandwidth yielded by the algorithms evaluated when applied to matrix i [15]. Metrics ρ β and ρ t employ function min because bandwidth reduction is a minimization problem.…”

Section: Description Of the Testsmentioning

confidence: 99%

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Oliveira

Silva

2021

RAIRO-Oper. Res.

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This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns.

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Section: Description Of the Testsmentioning

confidence: 99%

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Oliveira

Silva

2021

RAIRO-Oper. Res.

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“…There exist alternative algorithms for finding a peripheral vertex, including Arany's algorithm [1], but these algorithms are still computationally expensive when compared with a pseudoperipheral vertex finder. Consequently, many heuristics for bandwidth reductions require as a first step the determination of a pseudoperipheral vertex instead of determining a peripheral vertex as the initial vertex of the approach [15]. If, for a given u ∈…”

Section: Theoretical Background Definitions and Graph Notationmentioning

confidence: 99%

An Experimental Analysis of Three Pseudo-peripheral Vertex Finders in conjunction with the Reverse Cuthill-McKee Method for Bandwidth Reduction

Oliveira¹,

Abreu²

2019

Tend. Mat. Apl. Comput.

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The need to determine pseudoperipheral vertices arises from several graph-theoretical approaches for ordering sparse matrix equations. Results of two algorithms for finding such vertices, namely, the George-Liu and Kaveh-Bondarabady algorithms, are evaluated in this work along with a variant of the Kaveh-Bondarabady algorithm. Experiments among these three algorithms in conjunction with the Reverse Cuthill-McKee method suggest that the modified algorithm is a suitable alternative for reducing bandwidth of matrices that arise from specific application area, but it is dominated by the well-know George-Liu algorithm mainly when considering the computational times of the algorithms.

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Metaheuristic algorithms for the bandwidth reduction of large-scale matrices

Oliveira

Carvalho

2021

J Comb Optim

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Finding a Starting Vertex for the Reverse Cuthill-McKee Method for Bandwidth Reduction: A Comparative Analysis Using Asymmetric Matrices

Cited by 4 publications

References 29 publications

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

An Experimental Analysis of Three Pseudo-peripheral Vertex Finders in conjunction with the Reverse Cuthill-McKee Method for Bandwidth Reduction

Metaheuristic algorithms for the bandwidth reduction of large-scale matrices

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